A valve device for influencing pressure, in particular for regulating pressure, and/or an oil-separation device for separating oil out of blow-by gases may be arranged on a cylinder head cover of this type. In particular, a valve device and/or an oil-separation device can be fixed to an outer side of the cover body after production of the cover body of the cylinder head cover, for example by means of a clip-fit connection or a latching connection. Under certain operating conditions of the internal combustion engine, the fixing to the outer side of the cover body may lead to undesired icing or freezing of the valve device.